Example The sum of the numerator and denominator of a fraction is 11. If 1 is subtracted from he numerator and 2 is added to the denominator then the value of fraction. Find the fraction.
Solution:
Though you are looking for the fraction, you can not assume the fraction as 'x ',
(note this).
Letting the numerator be 'x'. By using the phrase ’the sum of numerator and
denominator is 11’ gives us
The denominator = (11  x ) \ The fraction =
Setting the equation as 
If 1 is subtracted from numerator and 2 is added to the denominator, then the value of fraction is
By cross multiplying, we get
3 ( x 1) = 1 ( 13  x )
3 x  3 = 13  x
\ 3 x + x = 13 + 3 . . . ( on transposing )
\ 4 x = 16
\ x = 4
Therefore, the required fraction =
Check:
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